Abstract
In some cases it is easier to describe what something is not, rather than what it is or what it wants to be. We shall therefore adhere to this principle when introducing this chapter.
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Bibliographical Notes
J. Guckenheimer, P. Holmes: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, 1983).
A. J. Lichtenberg, M. A. Lieberman: Regular and Stochastic Motion (Springer, 1983); 2nd edn: Regular and Chaotic Dynamics (Springer, 1992 ).
F. Verhulst: Nonlinear Differential Equations and Dynamical Systems (Springer, 1990).
P. Hagedorn: Nonlinear Oscillations, 2nd edn ( Clarendon Press, Oxford, 1988 ).
M. Tabor: Chaos and Integrability in Nonlinear Dynamics (Wiley, 1989).
E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations ( McGraw-Hill, New York, 1955 ).
J. K. Hale: Ordinary differential equations ( Wiley-Interscience, New York, 1969 ).
L. Cesari: Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations (Springer, 1971).
M. W. Hirsch, S. Smale: Differential Equations, Dynamical Systems and Linear Algebra (Academic Press, 1974).
E. Bessel-Hagen: Über die erhaltungssätze der Elektrodynamik, Math. Ann. 84, 258–276 (1921).
E. L. Hill: Hamilton’s principle and the conservation theorems of mathematical physics, Rev. of Mod. Phys. 23, 253–260 (1951).
A. Trautman: Noether equations and conservation laws, Commun. Math. Phys. 6, 248–261 (1967).
H. Rund: A direct approach to Noether’s theorem in the calculus of variations, Utilitas Mathematica 2, 205–214 (1972).
J. D. Logan: On some invariance identities of H. Rund, Utilitas Mathematica 7, 281–286 (1975).
Dj. S. Djukic: A procedure for finding first integrals of mechanical systems with gauge-variant Lagrangians, Int. J. Non-linear Mech. 8, 479–488 (1973).
Dj. S. Djukic, B. D. Vujanovic: Noether’s theory in classical nonconservative mechanics, Acta Mechanica 23, 17–27 (1975).
J. D. Logan: Invariant Variational Principles ( Academic Press, New York, 1977 ).
J. A. Kobussen: On a systematic search for integrals of the motion, Helvetica Physica Acta 53, 183–200 (1980).
V. G. Gurzadyan, G. K. Savvidy: Collective relaxation of stellar systems, Astron. Astrophys. 160, 203–213 (1986).
D. Boccaletti, G. Pucacco, R. Ruffini: Multiple relaxation time-scales in stellar dynamics, Astron. Astrophys. 244, 48–51 (1991).
P. Cipriani, G. Pucacco: Jacobi geometry and chaos in N-body systems, in Proceedings of the Workshop “From Newton to Chaos”, ed. by A. Roy ( NATO ASI, Cortina, 1993 ).
M. Pettini: Geometrical hints for a nonperturbative approach to Hamiltonian dynamics, Phys. Rev. E 47, 828–850 (1993).
M. Szydlowski: Curvature of gravitationally bound mechanical Systems, J. Math. Phys. 35, 1850–1880 (1994).
S. Bazanski, P. Jaranowski: The inverse Jacobi problem, J. Phys. A: Math. Gen. 27, 3221–3234 (1994).
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© 1996 Springer-Verlag Berlin Heidelberg
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Boccaletti, D., Pucacco, G. (1996). Dynamics and Dynamical Systems — Quod Satis. In: Theory of Orbits. Astronomy and Astrophysics Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03319-7_2
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DOI: https://doi.org/10.1007/978-3-662-03319-7_2
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